In a conventional UMTS system, a PDCCH (Physical Downlink Control Channel) message can use 1, 2, 4 or 8 Channel Control Elements (CCEs or resource elements)—referred to as CCE aggregation levels 1, 2, 4 or 8. A search space is a set of aggregated CCEs (with a certain aggregation level) within which a mobile station (or user equipment (UE) or secondary station) performs blind decoding of all PDCCH payloads possible for that aggregation level. Search spaces are defined per aggregation level; a secondary station in such a system thus can have up to four search spaces. For example, the search space of a UE for aggregation level 1 (referred to as 1-CCE) could consist of the CCEs indexed 3, 4, 5, 6, 7, 8, while its search space for aggregation level 8 could consist of the two resource sets of aggregated CCEs consisting of the CCEs indexed by 1, 2, . . . , 8 and 9, 10, . . . , 16, respectively. in this example, the UE thus performs six blind decodings for 1-CCEs and two blind decodings for 8-CCEs.
In an example, in order to determine the starting point of the search space, mobile stations (or secondary stations, also termed as UEs, for User Equipments in 3GPP parlance) compute a hash function f(UE_ID,s), where UE_ID is the identifier of the UE (different for distinct UEs) and s a time-varying subframe number. It is desirable that different UEs collide (have equal hash value) as infrequently as possible.
The hash function presently proposed within 3GPP is of the formf(UE_ID,s)=K(UE_ID*16+s)+L modulo M, 
where K, L and M are constants, UE ID is the identifier of the UE, and s is the subframe number. It is clear that with this particular hash function f, two UEs that collide for some subframe number collide persistently, i.e., for all subframe numbers.